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Bats spawn much like Spiders, clinging to the ceiling.
They will begin to fly at you if you move into the parabolic area below them, even if there is no line of sight.
Bats will always attempt to fly directly at you, with very little path-finding intelligence. If you move too far away from them or dive underwater they will stop pursuing and re-attach themselves to the ceiling.

The main difficulty when dealing with bats is that they tend to approach from above, where it can be difficult to hit them.
The best course of action is to run backwards or get to high ground, then wait for the bat to come to you. This will help to level the dangerous height difference and reduce the reliance on your reflexes.

Ideally, you should aim to draw the bat into a 45 degree angle between you and the ground, so that you can dispatch them by throwing an item upward at them, or at least bring them into the range of your jump-whipping.

Beware trapping yourself in a place where the bat will fly down directly on top of you: you won't be able to attack it unless you throw a rope, which is a waste of precious equipment.

It is important to be comfortable with jump-whipping to deal with bats easily.